Let \(E\)  denote the exponential radical of a connected complex Lie group \(G\) . (The terminology is from [1]}; the definition for a real connected Lie group is given in [2]}.) For the complex case we
use the following characterization as a definition:
\(E\)  is the normal complex Lie subgroup such that \(G/E\)  is
the largest quotient of \(G\)  that is locally isomorphic to a direct
product of a nilpotent and semisimple complex Lie group [3]}.
